Constructions and Bounds for Batch Codes with Small Parameters

2017 ◽  
pp. 283-295
Author(s):  
Eldho K. Thomas ◽  
Vitaly Skachek
Keyword(s):  
Small Parameters

Limit Cycle Bifurcations of a Planar Near-Integrable System with Two Small Parameters

2021 ◽  
Vol 41 (4) ◽  
pp. 1034-1056
Author(s):  
Feng Liang ◽  
Maoan Han ◽  
Chaoyuan Jiang
Keyword(s):  
Limit Cycle ◽  
Integrable System ◽  
Small Parameters

MATHEMATICAL BASIS OF COMPUTATIONAL PHYSICS

1996 ◽  
Vol 07 (03) ◽  
pp. 355-359 ◽  
Author(s):  
M. SUZUKI
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Quantum Monte Carlo ◽  
Computational Physics ◽  
Numerical Calculations ◽  
Symplectic Integration ◽  
Mathematical Basis ◽  
Small Parameters ◽  
Quantum Monte Carlo Simulations

The present paper explains some general basic formulas concerning quantum Monte Carlo simulations, symplectic integration and other numerical calculations. A generalization of the BCH formula is given with an application to the decomposition of exponential operators in the presence of small parameters.

scholarly journals Second-order differential equations with random perturbations and small parameters

2017 ◽  
Vol 147 (4) ◽  
pp. 763-779
Author(s):  
M. Kamenskii ◽  
S. Pergamenchtchikov ◽  
M. Quincampoix
Keyword(s):  
Differential Equations ◽  
Small Parameter ◽  
Random Perturbation ◽  
Stochastic Averaging ◽  
Second Order ◽  
Random Perturbations ◽  
Existence And Uniqueness Theorem ◽  
Second Order Differential Equations ◽  
Averaging Theorem ◽  
Small Parameters

We consider boundary-value problems for differential equations of second order containing a Brownian motion (random perturbation) and a small parameter and prove a special existence and uniqueness theorem for random solutions. We study the asymptotic behaviour of these solutions as the small parameter goes to zero and show the stochastic averaging theorem for such equations. We find the explicit limits for the solutions as the small parameter goes to zero.

scholarly journals THE INVESTIGATION OF DYNAMICS OF MISALIGNED UNITS IN VEHICLE TRANSMISSION

Transport ◽  
2002 ◽  
Vol 17 (6) ◽  
pp. 226-229
Author(s):  
Vytautas Turla ◽  
Igor Iljin
Keyword(s):  
Radial Direction ◽  
Parameter Method ◽  
Free Oscillations ◽  
Small Parameter Method ◽  
Mathematical Pendulum ◽  
Rotational Movement ◽  
Double Frequency ◽  
Shaft System ◽  
Small Parameters ◽  
Moment Of Resistance

In the article the problems related to the dynamics of a mechanic system on misalignment of shafts in radial direction are presented. The object of the investigation is a two-shaft system connected with an elastic centrifugal ring coupling. Using equations of static equilibrium it was found that an internal moment of resistance to rotation appears in the coupling connecting the radially misaligned shafts. Using Dalamber's principle for the rotational movement the differential equation that describes the rotation of the second shaft has been developed. It was shown that after the perfonnance of the corresponding actions and the introduction of a new variable the said equation is transformed in to an equation which character virtually coincides with the equation describing free oscillations of a mathematical pendulum. Because the value of misalignment of shafts in the radial direction is small in comparison with other parameters, a small parameter method was used for the solution of this equation. The found solutions show that rotational vibrations with the double frequency of rotational movement are excited in the misaligned mechanical system with an elastic centrifugal ring coupling. The restrictions ofthe application of a small parameters method have been explored and the limits of its application have been found.

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